7.1 Classification
147
a spheroid as an abstract molecule, as in the case of nematic phases. The distinction
from nematic phases is the existence of layers. If the degree of the layer formation
is high enough, each layer can be regarded as a two-dimensional fluid. However, it
is often the case that only the fundamental reflection is discernible experimentally.
In such cases, the naïve description of a smectic A phase as stacked layers of twodimensional fluid is not adequate.
Smectic phases having not the circular symmetry, but the six-fold symmetry
around the layer normal are known to exist. Such phases are termed smectic B (SmB)
phases. SmB phases are further divided into hexatic B (HexB) and crystal B (CrB)
phase. In the HexB phase, molecules are arranged roughly on a triangular lattice.
Since the spatial order in two-dimension is fragile, the arrangement cannot extend
over a long-range. There is no structural correlation between neighboring layers,
accordingly. In contrast, the spatial order in the CrB phase extends not only within
the layer but also to adjacent layers. For the reason that the spatial order extends in
three dimensions, the CrB phase is a kind of a three-dimensional crystal after the
definition by the International Union of Crystallography (IUCr) [5]. In comparison
with the SmA phase, the appearance of reflections indicating the triangular lattice
within the layer indicates the formation of these phases. Although reflections with
mixed indexes between hk0 (from the order within each layer) and 00l (from the
stack of layers) are expected for the CrB phase, such observation is rare. In practice,
HexB and CrB phases are discriminated through the assessment of the linewidth for
hk0 (narrower for CrB phase than for HexB phase).
Further lowering of the symmetry from the CrB phase results in another smectic
phase called the smectic E (SmE) or crystal E (CrE) phase. In this phase, the effective
molecular symmetry becomes of a brick (rectangular parallelepiped). Molecules
without distinctions between the head and tail and between the front and back form
herringbone arrays within respective layers, which stack on each other along the zaxis. The illustration certainly looks like a crystal of the orthorhombic system. This
resemblance is the reason why this phase is also called the crystal E phase. The CrE
phase seems an anisotropic counterpart of plastic crystals for globular molecules
while taking the assumed dynamical disorder into account. On the other hand, the
highly anisotropic shape of molecules suffices to pose a question of whether such
a disorder is possible. This issue is impossible to resolve by only considering the
averaged molecular shape. A possible resolution will be discussed in Sect. 9.4.4.2.
Although the orientation of the nematic director in the smectic phases mentioned
above coincides with the layer normal, which is the unique and rational direction
for the layered structure, there is generally no reason why they should coincide with
each other. Smectic C phase is a representative of such tilted smectic phases. Note
that there is no possibility for a uniformly tilted nematic phase because the uniform
tilt merely rotates the director. The tilt of the director from the layer normal induces
additional degrees of freedom. For example, the phase having the alternate tilt in
adjacent layers within a common plane perpendicular to the layer is called SmC A
phase in contrast to the simple SmC phase having uniform tilt within a common
plane. A wide variety can be imagined for the arrangement of the tilting in a layer
by layer. Even a successive twist of the tilt direction is possible.
147
a spheroid as an abstract molecule, as in the case of nematic phases. The distinction
from nematic phases is the existence of layers. If the degree of the layer formation
is high enough, each layer can be regarded as a two-dimensional fluid. However, it
is often the case that only the fundamental reflection is discernible experimentally.
In such cases, the naïve description of a smectic A phase as stacked layers of twodimensional fluid is not adequate.
Smectic phases having not the circular symmetry, but the six-fold symmetry
around the layer normal are known to exist. Such phases are termed smectic B (SmB)
phases. SmB phases are further divided into hexatic B (HexB) and crystal B (CrB)
phase. In the HexB phase, molecules are arranged roughly on a triangular lattice.
Since the spatial order in two-dimension is fragile, the arrangement cannot extend
over a long-range. There is no structural correlation between neighboring layers,
accordingly. In contrast, the spatial order in the CrB phase extends not only within
the layer but also to adjacent layers. For the reason that the spatial order extends in
three dimensions, the CrB phase is a kind of a three-dimensional crystal after the
definition by the International Union of Crystallography (IUCr) [5]. In comparison
with the SmA phase, the appearance of reflections indicating the triangular lattice
within the layer indicates the formation of these phases. Although reflections with
mixed indexes between hk0 (from the order within each layer) and 00l (from the
stack of layers) are expected for the CrB phase, such observation is rare. In practice,
HexB and CrB phases are discriminated through the assessment of the linewidth for
hk0 (narrower for CrB phase than for HexB phase).
Further lowering of the symmetry from the CrB phase results in another smectic
phase called the smectic E (SmE) or crystal E (CrE) phase. In this phase, the effective
molecular symmetry becomes of a brick (rectangular parallelepiped). Molecules
without distinctions between the head and tail and between the front and back form
herringbone arrays within respective layers, which stack on each other along the zaxis. The illustration certainly looks like a crystal of the orthorhombic system. This
resemblance is the reason why this phase is also called the crystal E phase. The CrE
phase seems an anisotropic counterpart of plastic crystals for globular molecules
while taking the assumed dynamical disorder into account. On the other hand, the
highly anisotropic shape of molecules suffices to pose a question of whether such
a disorder is possible. This issue is impossible to resolve by only considering the
averaged molecular shape. A possible resolution will be discussed in Sect. 9.4.4.2.
Although the orientation of the nematic director in the smectic phases mentioned
above coincides with the layer normal, which is the unique and rational direction
for the layered structure, there is generally no reason why they should coincide with
each other. Smectic C phase is a representative of such tilted smectic phases. Note
that there is no possibility for a uniformly tilted nematic phase because the uniform
tilt merely rotates the director. The tilt of the director from the layer normal induces
additional degrees of freedom. For example, the phase having the alternate tilt in
adjacent layers within a common plane perpendicular to the layer is called SmC A
phase in contrast to the simple SmC phase having uniform tilt within a common
plane. A wide variety can be imagined for the arrangement of the tilting in a layer
by layer. Even a successive twist of the tilt direction is possible.